Abstract
We study the limit theorem related to the interface of the three-dimensional Ising model. Dobrushin proved that the interface does not fluctuate and becomes rigid for sufficiently largeβ. We define the random fieldX L(t, s), 0⩽t, s⩽1, on the interface, and prove that XL(t, s) converges to the Brownian sheet as L→∞ for sufficiently largeβ, whereL denotes the size of the system. This result does not mean that the interface itself converges to the Brownian sheet.
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Kuroda, K., Manaka, H. The interface of the Ising model and the Brownian sheet. J Stat Phys 47, 979–984 (1987). https://doi.org/10.1007/BF01206172
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DOI: https://doi.org/10.1007/BF01206172